Question

If the roots of the equation $a{x}^2+bx+c=0$ are reciprocal of each other, then

• A. $a=b$
• B. $a=c$
• C. $b=c$
• D. $a=0$

Answer 1

Answer: (B)

$a=c$

For the equation, $a{x}^2+bx+c=0$. Let the roots be $\alpha$ and $\frac{1}{\alpha }$
Now, product of roots = $\left(\alpha \right)\left(\frac{1}{\alpha }\right)$ = $\frac{c}{a}$
$1=\frac{c}{a}$
$a=c$